Depends 
The basic use of sampling is that indeed : you "record" a sound, and play it back later.
But if it were only that, the use of samplers would be dead by now, because of the power of today's sequencers. Why use a dedicated hardware or software sampler, if you can just set an instance of a recorded sound in an audio track in your sequencer?
Nowadays, samplers are more capable than that. The funny part is, that samplers are made out of two parts really : the sampling part, and the synthesizing part.
The sample part is the easiest part : it's basically the recording of the sample, the editing (like you would in soundforge for example) and the playback.
The synthesizing part is called this way, because it uses the architecture of a "regular" synthesizer. You have your sound source with a synth it's an oscillator, in the sampler it's your samples), followed by a filter, and an amp. Those can be controlled by envelopes. Most samplers also have LFO's to control several parameters, and effects can be added. You see, that with this already, more complicated stuff than basic playback can be made.
But...
The most important part (for me) nowadays, is multisampling.
Take a real piano for example. It has lots of keys (88 standard). Tap one key, tap another. It's not only the note that changes in pitch. But the harmonic content also changes (ie a high note doesn't sound the same as a low note just pitched up). Same goes for the force you tap the keys. If you slam it hard, it's not only volume that changes. The hard note will seem to have a more powerful attack.
The first samplers didn't really account for this. You sampled one piano note, and you spread it out the keyboard (samplers are controlled via MIDI). The problem was, only the notes around the root key (the "original note" you sampled) sounded good. Once you got further away, it started to sound unnatural, because the notes were pitched up/down.
Same goes for velocity. One sample was used, you tap your midi keyboard harder or softer, and the only difference you hear is the volume of the sample that changes. The actual sound of the sample doesn't change. This is called the machine gun effect (think of a snare or drum roll with always the same sample, very unnatural, sounds like the ratatatata of a machine gun).
So here comes multisampling. Here you take different samples for different notes and different velocities. The more values you have (in midi max 127 of course), the more natural it will sound.
Take a perfect sample library for example, piano again. The people who made it, were very thorough with it, and sampled each key of the piano, and each key tapped at 128 different "forces" (the 128 velocities of midi). Huge sample library of course.
But now you play on your midi keyboard. You play C3, it will sound like the C3 of the piano. You play D4, and it will sound like the D4 of the piano, not like a pitched up C3.
Same goes with the velocities. Humans are no robots, so they can't actually apply exactly the same force each time they play a note. So the sound will change with each note (try playing the same note repeatedly on a real piano and listen). So it's only natural that if you play it on your midi keyboard that the sound will change like it would on a real piano, not always the exact same note. That's the velocity layering you always read about.
So key mapping and velocity layering are very important in sampling nowadays. But with good samplers and good sampling libraries (Vienna Symphonic Library is about the most powerful in that regard) can go further than that. For example, the upwards stroke of a violin, doesn't sound exactly the same as the downwards one. Pizzicato is not the same as spiccato. So good samplers and libraries can integrate tools to do the switching between different styles of play.
And of course, if you look at Kontakt, sound mangling is one of it's main forces too. Timestretching, beat mapping, all can be done with it.
So saying samplers are only used to "play" sampled sounds, is really looking at it in a limited way. Nowadays, you can safely say that samplers are as powerful as synthesizers.
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